Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular sp

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3-2.Motion in Plane

hard

Two particles $A, B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega $. At $t = 0,$ their positions and direction of motion are shown in the figure

The relative velocity $\overrightarrow {{V_A}} - \overrightarrow {{V_B}} $ at $t = \frac{\pi }{{2\omega }}$ is given by

A

$\omega ({R_1} + {R_2})\,\hat i$

B

$-\omega ({R_1} + {R_2})\,\hat i$

C

$\omega ({R_2} - {R_1})\,\hat i$

D

$\omega ({R_1} - {R_2})\,\hat i$

(JEE MAIN-2019)

Solution

at $t= 0$ $at\,t = \frac{\pi }{{2\omega }}$

${\overrightarrow V _A} = {\overrightarrow V _B} = – \omega {R_1}\hat i + \omega .{R_2}\hat i$

$ = \omega \left( {{R_2} – {R_1}} \right)\hat i$

Standard 11

Physics

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